Numberlines

A numberline helps people visualize numbers. It is a nice way to add and subtract small numbers. If you've never seen them before they can be confusing, so here's a look at how to use a numberline.

To add 2 numbers: find the first number on the numberline. Now jump forward as many jumps as the second number. Check what number you ended your jumps at. That is the answer.

Example: 5+4

Find 5 and place your pencil there.

a numberline ranging from 1 to 17 with 5 circled

Now jump 4 numbers forward (to the right).

a numberline with 5 circled and a bumpy line hopping from 5 to nine

You are at 9. So 5 + 4 = 9.

a numberline ranging from 1 to 17 with 5 circled, a bumpy line hopping from 5 to 9, and an arrow pointing at 9

Or you can use a small counter or character to do the addition. Here is 5+4 with a duck.

a numberline ranging from 1 to 17 with 5 circled and a duck above the 5

a numberline ranging from 1 to 17 with 5 circled and a duck at 9 with buppy lines showing the duck's hops

To subtract: find the first number, now hop left (toward smaller numbers) as many times as the number you are subtracting. The number you end at is your answer.

Lets look at 14 -6

Find 14.

Now "hop" left 6 spaces.

a numberline with 14 circled, a bumpy line above the section between 8 and 14, and the number 8 underlined

You've arrived at 8, so 14 - 6 = 8

Negative numbers

A numberline can be a big help visualizing how negative numbers interact with addtion and subtraction. The duck is helpful here. If you add a positive number, the duck faces the positive direction (right) and moves forward.
Here is 5 + 4 = 9

a numberline ranging from 1 to 17 with 5 circled and a duck at 5.

If you subtract a positive number, the duck is still facing the postive direction but moves backwards. Here is 4 - 3 = 1
a numberline ranging from -6 to 10 with 4 circled and a duck at 4
If you want to add or subtract a negative number, the duck is backwards, but still moves in the head directions for addition or the tail direction for subtraction.

Here we have -2 + -3 = -5
a numberline ranging from -6 to 10 with a duck facing left at -2

And now to subtract a negative here is -2 - -4 = 2 a numberline ranging from -6 to 10 with a duck facing left at -2 The duck faces the negative end of the numberline because the 2nd number is negative and moves backwards because we are subtracting. a numberline with a duck at -2 and a bumpy line showing 4 jumps right to 2 a numberline with a duck at 2 and a bumpy line showing 4 jumps from -2 right to 2

And that's how to add and subtract with a numberline and a duck.